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A047617
Numbers that are congruent to {2, 5} mod 8.
19
2, 5, 10, 13, 18, 21, 26, 29, 34, 37, 42, 45, 50, 53, 58, 61, 66, 69, 74, 77, 82, 85, 90, 93, 98, 101, 106, 109, 114, 117, 122, 125, 130, 133, 138, 141, 146, 149, 154, 157, 162, 165, 170, 173, 178, 181, 186, 189, 194, 197, 202, 205, 210, 213, 218, 221, 226, 229, 234
OFFSET
1,1
COMMENTS
Numbers whose binary reflected Gray code (A014550) ends with 11. - Amiram Eldar, May 17 2021
FORMULA
a(n) = 8*n - a(n-1) - 9 (with a(1)=2). - Vincenzo Librandi, Aug 06 2010
a(n) = 4*n - (5 + (-1)^n)/2. - Arkadiusz Wesolowski, Sep 18 2012
G.f.: (2+3*x+3*x^2)/((-1+x)^2*(1+x)). - Harvey P. Dale, Feb 23 2016
a(1)=2, a(2)=5, a(3)=10, a(n) = a(n-1) + a(n-2) - a(n-3). - Harvey P. Dale, Feb 23 2016
From Franck Maminirina Ramaharo, Jul 22 2018: (Start)
a(n) = A047470(n) + 2.
E.g.f.: (6 - exp(-x) + (8*x - 5)*exp(x))/2. (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(2)*Pi/16 - log(2)/8 + sqrt(2)*log(sqrt(2)+1)/8. - Amiram Eldar, Dec 11 2021
MATHEMATICA
Select[Range[300], MemberQ[{2, 5}, Mod[#, 8]]&] (* or *) LinearRecurrence[ {1, 1, -1}, {2, 5, 10}, 80] (* Harvey P. Dale, Feb 23 2016 *)
PROG
(Maxima) makelist(4*n -(5 + (-1)^n)/2, n, 1, 100); /* Franck Maminirina Ramaharo, Jul 22 2018 */
(Python)
def A047617(n): return (n-1<<2)+1+(n&1) # Chai Wah Wu, Mar 30 2024
KEYWORD
nonn,easy
EXTENSIONS
More terms from Vincenzo Librandi, Aug 06 2010
STATUS
approved